document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=619963>Question 619963</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Hi, I've been stuck on this question all day! Hoping I could get some help:\r<BR>\n" );
document.write( "\n" );
document.write( "Whats the height of college hockey players? The avg height has been 68.3 inches. A random <BR>\n" );
document.write( "sample of 14 hockey players gave a mean height of 69.1 inches. We may assume that x has a normal distribution with std dev of 0.9 inch. Does this indicate that the population mean height is <BR>\n" );
document.write( "different from 68.3 inches? Use 5% level of significance \r<BR>\n" );
document.write( "\n" );
document.write( "and this one as well please:\r<BR>\n" );
document.write( "\n" );
document.write( "A random sample of 83 investment portfolios managed by Kendra showed that 62 of them met the targeted annual percent growth. A random sample of 112 portfolios managed by Lisa showed that 87 met the targeted annual percent growth. Find a 99% confidence interval for the difference in the proportion of the portfolios meeting target goals managed by Kendra compared with those managed by Lisa. Is there a difference in the proportions at the 99% confidence level? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #390067 by </B><A HREF=/tutors/aboutme.mpl?userid=stanbon><B>stanbon(75887)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=stanbon><IMG SRC=http://www.algebra.com/images/aboutme-small.gif BORDER=0 alt=\"About Me\" VALIGN=MIDDLE></A>&nbsp;<IMG SRC=http://www.algebra.com/images/nopicture.jpg><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=390067\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> What is the height of college hockey players? The avg height has been 68.3 inches. <BR>\n" );
document.write( "A random sample of 14 hockey players gave a mean height of 69.1 inches. We may assume that x has a normal distribution with std dev of 0.9 inch. Does this indicate that the population mean height is <BR>\n" );
document.write( "different from 68.3 inches? Use 5% level of significance<BR>\n" );
document.write( "Ho: u = 68.3 (claim)<BR>\n" );
document.write( "Ha: u # 68.3<BR>\n" );
document.write( "-----<BR>\n" );
document.write( "t(69.1) = (69.1-68.3)/[0.9/sqrt(14)] = 0.2138<BR>\n" );
document.write( "p-value = 2*p(0.2138< = t <= 100 when df = 13) = 2*tcdp(0.2138,100,13)<BR>\n" );
document.write( "= 0.4170<BR>\n" );
document.write( "----<BR>\n" );
document.write( "Since the p-value is greater than 5%, fail to reject Ho.<BR>\n" );
document.write( "The mean height is 68.3.<BR>\n" );
document.write( "=================================\r<BR>\n" );
document.write( "\n" );
document.write( "A random sample of 83 investment portfolios managed by Kendra showed that 62 of them met the targeted annual percent growth. A random sample of 112 portfolios managed by Lisa showed that 87 met the targeted annual percent growth. <BR>\n" );
document.write( "--------<BR>\n" );
document.write( "Find a 99% confidence interval for the difference in the proportion of the portfolios meeting target goals managed by Kendra compared with those managed by Lisa.<BR>\n" );
document.write( "--------<BR>\n" );
document.write( "Is there a difference in the proportions at the 99% confidence level?<BR>\n" );
document.write( "---<BR>\n" );
document.write( "Kendra DATA:<BR>\n" );
document.write( "sample proportion = phat2 = 62/83 = 0.75<BR>\n" );
document.write( "Lisa DATA:<BR>\n" );
document.write( "sample proportion = phat1 = 87/112 = 0.78<BR>\n" );
document.write( "------<BR>\n" );
document.write( "Ho: p1 - p2 = 0<BR>\n" );
document.write( "Ha: p1 - p2 # 0<BR>\n" );
document.write( "---------------------------------<BR>\n" );
document.write( "std of proportion differences: sqrt[(p1q1/n1) + (p2q2/n2)] <BR>\n" );
document.write( "= sqrt[(.75*0.25/83)+(0.78*0.22/112)] = 0.0616<BR>\n" );
document.write( "---------------------------------------------------<BR>\n" );
document.write( "z(difference) = (0.78-0.75)/0.0616 = 0.4872<BR>\n" );
document.write( "----<BR>\n" );
document.write( "sample proportion difference = 0.03<BR>\n" );
document.write( "std of sample difference: sqrt[(0.75*0.25/83)+(0.78*0.22/112)] = 0.0616<BR>\n" );
document.write( "-----<BR>\n" );
document.write( "Margin of error: 2.5758*0.0616 = 0.1586<BR>\n" );
document.write( "------<BR>\n" );
document.write( "99% CI: 0.03-0.1586 < p1-p2 < 0.03+0.1586<BR>\n" );
document.write( "(-0.1286 , +0.1886)<BR>\n" );
document.write( "===========<BR>\n" );
document.write( "Conclusion: Since zero is in the 99% CI, fail to reject Ho.<BR>\n" );
document.write( "===============================<BR>\n" );
document.write( "Cheers,<BR>\n" );
document.write( "Stan H.<BR>\n" );
document.write( "=============================================\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );